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Former ISIS fighter speaks exclusively to CNN

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ISIS plans to take over the Arab world and then "go to other countries," an ex-fighter says

The man left the radical terror group two weeks ago

"Since Western fighters joined ISIS, they consider their home country as infidels," he says

To the outside world, they're a force of ruthless yet mysterious insurgents bent on terrorizing civilians and expanding Islamist rule.

But as one former ISIS fighter tells CNN, the mentality goes much deeper.

"The main and principal goal of the Islamic State that they tell their new members is to establish an Islamic state that will encompass the Arab world," the man said in Turkey. "And after that, we go to other countries."

Just two weeks ago, the man was in Raqqa, the ISIS stronghold in northern Syria. Like many cities across Syria and Iraq, Raqqa has been overrun by ISIS militants who show no mercy for those who don't follow their hard line.

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Crucifixions and public executions take place virtually every day. Women not fully covered in niqabs are lashed with alarming frequency.

Even store owners who leave their shops open during times of prayer can get beaten or sent to prison.

The former insurgent, in his 20s, left ISIS two weeks ago because he said the group is "spreading injustice in the name of justice."

But he still agrees with the ideology of the group that is forcing its beliefs on everyday life, including in education.

"Philosophy is prohibited; they canceled it as a kind of blasphemy," he said. "Many subjects have been canceled, like music and even sometimes sports. All of them have been canceled from the school curriculum."

Perhaps the only thing as disturbing as ISIS' terror rampage is the growing number of foreigners joining its ranks.

Thousands of foreign fighters are estimated to have joined ISIS. And the ex-ISIS militant said these foreigners could carry out attacks when they go home, but security measures in those countries could make it difficult -- at least for now.

"Since Western fighters joined ISIS, they consider their home country as infidels," he said. "If they have a chance, they will carry out attacks."

And the United States got a harsh reminder of ISIS' reach when Douglas McAuthur McCain, a 33-year-old from the Midwest, became the first known American to be killed while fighting for ISIS.

U.S. Defense Secretary Chuck Hagel has called ISIS "beyond just a terrorist group."

"They marry ideology, a sophistication of strategic and tactical military prowess," he said last week. "This is beyond anything we have seen, and we must prepare for everything."

ISIS may have wanted to show off its global reach by having a militant with a British accent front the videos of the beheadings of American journalists James Foley and Steven Sotloff.

And that kind of tactic could also inspire more foreigners, the former ISIS fighter told CNN.

"It is possible that the goal was to project the image that a European, or a Western person, executed an American so that they can showcase their Western members and appeal to others outside Syria and make them feel that they belong to the same cause."